Journal of Mathematical Sciences

, Volume 200, Issue 1, pp 1–11 | Cite as

On the Transform of a Guidance Game

  • Yu. V. Averboukh


This paper is devoted to the study of the structure of solutions of the differential guidance game in the case where the objective set is contained in the position space and is the controllability set for some control system.


Feedback Strategy Game Problem Program Iteration Stable Bridge Piecewise Constant Control 
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  1. 1.
    A. A. Agrachev and Yu. V. Sachkov, Geometric Control Theory [in Russian], Fizmatlit, Moscow (2005).Google Scholar
  2. 2.
    Yu. V. Averbukh, “On the problem of guidance of an autonomous conflict-controlled system onto a cylinder set,” Cybern. Syst. Anal., 44, No. 5, 729–737 (2008).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    A. G. Chentsov, “On the structure of a game problem of convergence,” Sov. Math. Dokl., 16, 1404–1408 (1976).Google Scholar
  4. 4.
    A. G. Chentsov, “On a game problem of convergence at a give time instant,” Mat. Sb., 99, No. 3, 394–420 (1976).MathSciNetGoogle Scholar
  5. 5.
    A. G. Chentsov, “On a guidance game,” Dokl. Akad. Nauk SSSR, 226, No. 1, 73–76 (1976).MathSciNetGoogle Scholar
  6. 6.
    A. G. Chentsov, Method of program iterations for a differential game of convergence/divergence [in Russian], Preprint VINITI 1933-79Dep (1979).Google Scholar
  7. 7.
    S. V. Chistyakov, “On solving pursuit game problems,” J. Appl. Math. Mech., 41, 845–852 (1979).CrossRefMATHGoogle Scholar
  8. 8.
    N. N. Krasovskii, “Differential game of convergence/divergence, I” Izv. Akad. Nauk SSSR, Ser. Tekhn. Kibernet., 2, 3–18 (1973).MathSciNetGoogle Scholar
  9. 9.
    N. N. Krasovskii and A. I. Subbotin, “An alternative for the game problem of convergence,” J. Appl. Math. Mech., 34, 948–965 (1970).CrossRefMathSciNetGoogle Scholar
  10. 10.
    N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).Google Scholar
  11. 11.
    N. N. Krasovskii and A. I. Subbotin, Game-Theoretical Control Problems, Springer-Verlag, New York (1988).CrossRefMATHGoogle Scholar
  12. 12.
    A. A. Melikyan, “Value function in the linear differential game of convergence,” Dokl. Akad. Nauk SSSR, 237, No. 3, 521–524 (1977).MathSciNetGoogle Scholar
  13. 13.
    I. M. Mitchel, A. M. Bayen, and C. J. Tomlin, “A time-depend Hamilton–Jacobi formulation of reachable sets for continuous dynamic games,” IEEE Trans. Automat. Control, 50, No.7, 947–957 (2005).CrossRefMathSciNetGoogle Scholar
  14. 14.
    A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems [in Russian], Nauka, Moscow (1981).Google Scholar
  15. 15.
    V. I. Ukhobotov, “Construction of a stable bridge for one class of linear games,” Prikl. Mat. Mekh., 41, No.2, 358–364 (1977).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia

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